We study correlations originating from the quantum nature of gluons in a hadronic wave function.
Bose-Einstein correlation between identical particles lead to the enhancement
in the number of pairs of gluons with the same quantum numbers and small relative momentum.
We show that these preexisting correlations can be probed in Deep Inelastic Scattering experiments at high energy.
Specifically, we consider diffractive trijet production. The azimuthal dependence
displays a peak at the zero relative angle between the transverse momentum imbalance of the photon-going dijet and
the transverse momentum of the hadron-going jet.
Our calculations explicitly show that the strength of the peak depends dramatically on the difference between the magnitudes of both transverse vectors.
Comparing electron-proton to electron-nucleus collisions,
we demonstrate that the nuclear target
enhances the relative strength of the peak
originating from Bose enhancement.
With the future high luminosity Electron-Ion Collider the proposed measurements of gluon Bose enhancement
become experimentally feasible.


Introduction.
The future Electron-Ion Collider will provide a unique opportunity to explore the multi-dimensional structure of protons and nuclei [1]}, [2]}.
Although most of the experimental measurements and theoretical studies are focused on single-parton distributions [3]}, [4]}, [5]}, [6]},
complete theoretical and experimental understanding of a hadron wave function is not possible without observables sensitive to multi-parton correlations. The simplest objects that probe such correlations
are multi-parton distribution functions [7]}, [8]}, [9]}, [10]}, [11]} and generalized parton distributions [12]}, [13]}.
Among these, gluon distributions play the most important role in high energy collisions. Indeed,
the measurements at HERA established that
the small x The Bjorken \(x\)  is the longitudinal momentum fraction of the hadron carried by a gluon. tail of the hadronic wave function is dominated by gluons [14]}, [15]}, [16]}, [17]}.
Thus it is imperative to identify observables sensitive to multi-gluon correlations.
The universal source of correlations between (identical) gluons is Bose enhancement due to quantum statistics. In the hadron wave function this induces the enhancement
in the number of pairs of gluons with the same quantum numbers and small relative momentum [18]}, [19]}, [20]}. These Bose-Einstein correlations have been suggested as a possible mechanism for producing ridge correlations in p-p scattering [19]}, [22]}, however strong final state interactions make their effect difficult to isolate.
Here we show that these correlations can be probed in a clean straightforward way in Deep Inelastic Scattering (DIS) experiments. We also observe that the effect due to these correlations is enhanced by saturation effects in the target hadron.
